Help on choosing truncation distance and binning strategy
C. Canonne
Hello DS community,
I would appreciate your advice on choosing truncation distance and binning strategy for detection function analyses, especially given the strong heaping I observe in the tail of my distance data.
I am currently working with three different datasets. I may eventually combine them on the subset of shared sites, but for now I am fitting detection functions separately on each full dataset.
My main issue is that estimated density changes substantially when I modify the truncation threshold, making results highly sensitive to the chosen cutoff.
In the attached HTML file:
section 2 shows the raw distance distributions by dataset (full season vs July only),
section 3 contains some diagnostic plots that may be helpful.
I would especially welcome recommendations on:
choosing truncation distance and number of bins,
and whether variable bin widths (e.g. larger bins in the tail) would help with the heaping pattern.
Best regards,
Coline Canonne
Laura Marshall
Thank you for your query and for sharing examples of your data. I can see that there is some rounding in the data — probably to the nearest 5m up to 50m, and then to the nearest 10m after that. You do have fairly long tails in your data, so truncation should help make detection function estimation more reliable.
When distances have been rounded, it can help to use bins in the analysis. If the data are rounded to the nearest 5m (up to 50m) then 10m (beyond 50m), I would use bins corresponding to 0–2.5m, 2.5–7.5m, 7.5–12.5m... 47.5–55m, 55–65m, etc., so that the heaped distances fall in the middle of the bins. With this many bins, however, we would not expect much difference between this approach and modelling them as exact distances. It may make some small difference to model goodness-of-fit assessment.
Regarding truncation, you have seen that the Introduction to Distance Sampling book suggests a truncation distance where the probability of detection is ~0.15. I think this is a reasonable rule of thumb. You would fit a basic detection function to your data and determine the corresponding distance, as you have done. We would often recommend a half-normal detection function for this purpose, but looking at some of your histograms, which fall away more steeply, a hazard rate might be more appropriate. While this truncation may feel fairly severe for some of your data, I have found that it can help provide more reliable estimates — especially when there are covariates affecting detectability that are not accounted for in the detection function.
We have a vignette on our website looking at how truncation distance affects estimation: https://distancesampling.org/dsims/articles/dsims-examples.html. This vignette examines a scenario where a covariate greatly affects detectability, and explores the effects of different truncation distances when this covariate is both excluded and included in the detection function model. I would expect the effects in real-world surveys to be less extreme than this, but it could help explain why your choice of truncation distance is leading to substantially different density estimates.
I hope this is of some help.
Best wishes,
Laura